κ = 8.04849251275843e-4: #359's post-Design-T kernel/retime/reorders on our reordered-design base (+0.068%)

[rohanarun]

Conditional κ = 804849251275843/10¹⁸ ≈ 8.04849251275843e-4, +5.46e-7 (+0.068 %) over #359 (8.04303459176812e-4).

Stacked on #359 (chafreaky). The complex supplier is unchanged: Sussman's E8 unit. The bit side binds.

This composes two independent gains:

• our κ = 8.03654539036015e-4: #354's staged Design T + twins on a reordered-design p10b base word (+0.064%) #357: Conditional κ = 7.696840393833340e-4: a stronger p = 10 bit word — re-annealed pair module, p = 10 local design, balanced cube orientation, tiered reuse matching (+0.71% over #315's word) #325's producer with the design list reordered and PLAIN = 12, Conditional κ = 7.76518649004426·10⁻⁴: the full transcript stage stack on #325's p10b word, priced against #327's p = 10 complex supplier (+0.888% over #325) #329's stages re-derived on that word, then Design T + twins (470 twins);
• chafreaky's Conditional κ = 8.04303459176812·10⁻⁴: kernel, retiming and reorders re-derived on #354's Design T word (+0.0776 % over #358) #359: the post-Design-T stages, re-derived on that Design T word with Conditional κ = 8.04303459176812·10⁻⁴: kernel, retiming and reorders re-derived on #354's Design T word (+0.0776 % over #358) #359's own discovery tools.

stage	this PR	#359
shared-donor kernel	335 entries, rank 440, φ −403.88	323, 435, −386.03
retiming	93 gates, φ −48.79	47, −49.68
reorders	130 + 2 (φ −296.89, −5.55), then 0	130 + 2

Every stage passes stagelib.full_check (legality, exact frames and nondegeneracy, formal F2 of every column, source spans). The bit coarse saving comes from both engines, and #315's outer assembly gives 47 strict constraints, all positive.

Draft: the full verify.sh replay is running, and I'll post the PASS line here.

🤖 Generated with Claude Code

https://claude.ai/code/session_01TGoMCHAqctZe4wtb4qr7vv

[rohanarun]

Full replay: bash research/w3-design-t-staged-p10b-reorder-k/verify.sh /tmp/out → PASS conditional kappa = 804849251275843/1000000000000000000 = 0.000804849251275843 (all stages: manifest, staged/parity hashes, Design T + twins rebuild, kernel/retime/reorders with full checks, #266 legality and five-stage columns, nondegeneracy, bank tiling, E8 complex b, outer assembly).

[Mister-Meeseeks]

Thank you @rohanarun. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Parallel reordered-base composition with post-Design-T stages.

Review and limits: The inherited CI only tests the older package. Direct replay is required for this distinct directory; stale DRAFT wording is preserved as historical, not a current result statement.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: f46ddb51f66381a1668da3801bb1632aacebe224. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.